By default, WordPress indeed doesn’t allow uploading of SVG files. To be able to add SVG support, you have to install the SVG Support plugin. https://wordpress.org/plugins/svg-support/
Once you’ve installed this plugin, you’ll be able to use SVG files just like any other image files supported by WordPress.
Can you check for any errors that might be causing it?
You might also want to try updating some plugins and see if it solves the issue.
Here’s a working demo w/ WordPress 5.5.1 on SVG Support 2.3.18. (GenerateBlocks 1.1.2, GP Premium 1.11.3, GP 2.4.2) https://share.getcloudapp.com/p9uGZwGN
By the way, you can also try to add backgrounds on general common areas by activating “Backgrounds” on GP Premium. https://share.getcloudapp.com/Jru6egG9